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A long-standing goal in neuroscience has been to bring together neuronal recordings and neural network modeling to understand brain function. Neuronal recordings can inform the development of network models, and network models can in turn provide predictions for subsequent experiments. Traditionally, neuronal recordings and network models have been related using single-neuron and pairwise spike train statistics. We review here recent studies that have begun to relate neuronal recordings and network models based on the multi-dimensional structure of neuronal population activity, as identified using dimensionality reduction. This approach has been used to study working memory, decision making, motor control, and more. Dimensionality reduction has provided common ground for incisive comparisons and tight interplay between neuronal recordings and network models., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending on the spatial scales of recurrent and feedforward connectivity. We close by showing how these ideas, together with plasticity rules, can help to close the loop between network structure and activity statistics., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

The brain must both react quickly to new inputs as well as store a memory of past activity. This requires biology that operates over a vast range of time scales. Fast time scales are determined by the kinetics of synaptic conductances and ionic channels; however, the mechanics of slow time scales are more complicated. In this opinion article we review two distinct network-based mechanisms that impart slow time scales in recurrently coupled neuronal networks. The first is in strongly coupled networks where the time scale of the internally generated fluctuations diverges at the transition between stable and chaotic firing rate activity. The second is in networks with finitely many members where noise-induced transitions between metastable states appear as a slow time scale in the ongoing network firing activity. We discuss these mechanisms with an emphasis on their similarities and differences., (Copyright © 2017 Elsevier Ltd. All rights reserved.)